Quantification of spatiotemporal phenomena by means of cellular automata techniques

Quantification methods for spatiotemporal patterns are introduced, which are based on nearest-neighbor considerations inspired by cellular automata as well as by more complex spatiotemporal dynamics. In particular, spatial and temporal structures, which can be found in aggregation and clustering phenomena, are quantified by introducing the concept of cellular automata (CA) measures for homogeneity and for the amount of fluctuations contributing to the observed dynamics. The aim of this paper is to define such measures and then test their performance on theoretically generated data sets. These tests with exemplary spatiotemporal patterns show the applicability of these methods for data analysis. For example, with the help of the CA fluctuation number we are able to extract the amount of noise present in spatiotemporal data. The observables constructed with the help of such CA techniques have straightforward applications in life sciences, where the quantitative analysis of spatiotemporal patterns still suffers from the lack of a standardized set of analysis techniques.